Abstract

By a proper design of the frequency-dependent gain characteristic of optical amplifiers, the parameters (amplitude η and velocity κ) of optical solitons in fibers can be made to approach a desired fixed point in κη space. The method is effective in controlling the random walk of solitons caused either by initial jitter and/or by amplifier noise (the Gordon–Haus effect) and in overcoming the bit-rate limitation that they provide.

© 1992 Optical Society of America

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References

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  1. J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  2. M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
    [CrossRef] [PubMed]
  3. For a choice of ω0 not at the peak of the gain curve, ∂g/∂ω ≠ 0. In this case the stable sink in Fig. 1 appears at a point with κ ≠ 0. However, this result is incompatible with the assumption of slowly varying gain curve.
  4. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990); Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef] [PubMed]
  5. A. Hasegawa, Y. Kodama, Opt. Lett. 16, 1385 (1991).
    [CrossRef] [PubMed]
  6. L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
    [CrossRef]
  7. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  8. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]

1991 (2)

A. Hasegawa, Y. Kodama, Opt. Lett. 16, 1385 (1991).
[CrossRef] [PubMed]

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

1990 (2)

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990); Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

1987 (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

1986 (1)

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

Kodama, Y.

Kubota, H.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Kurokawa, K.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Yamada, E.

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

IEEE J. Lightwave Technol. (1)

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, IEEE J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (1)

For a choice of ω0 not at the peak of the gain curve, ∂g/∂ω ≠ 0. In this case the stable sink in Fig. 1 appears at a point with κ ≠ 0. However, this result is incompatible with the assumption of slowly varying gain curve.

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Figures (2)

Fig. 1
Fig. 1

Flow (solid curves) and equipotential (dashed curves) lines in the xy plane determined by the dynamical equations (12) and (13). Note that for a given value of β and δ, the soliton amplitude (η) and velocity (κ) acquire a stable fixed value designated by the sink (0, 1).

Fig. 2
Fig. 2

Reduction factor f(x) [Eq. (28)] of the variance of the arrival time jitter 〈T02〉 by the present method.

Equations (28)

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g ( ω ) = g ( ω 0 ) + g ω | ω = ω 0 ( ω ω 0 ) + 1 2 2 g ω 2 | ω = ω 0 ( ω ω 0 ) 2 .
i E z 1 2 k E τ 2 + ω 0 n 2 2 c | E | 2 E = i [ γ g ( ω 0 ) ] E i g 2 2 E τ 2 .
i q Z + 1 2 2 q T 2 + | q | 2 q = i ( Γ G ) q i G 2 q T 2 .
q ( T , Z ) = a ( Z ) u ( T , Z ) ,
d a d Z = [ Γ + δ G ( Z ) ] a .
υ Z i 2 2 υ T 2 i | υ | 2 υ = δ υ β 2 υ T 2 + O ( Z a 2 ) .
υ ( T , Z ) = η sech η ( T + κ Z ) × exp [ i κ T + i 2 ( η 2 κ 2 ) Z ] ,
d d Z | υ | 2 d T = 2 δ | υ | 2 d T + 2 β | υ T | 2 d T
d d Z ( υ * υ T υ υ * T ) d T = 2 δ ( υ * υ T υ υ * T ) d T 2 β ( 2 υ * T 2 υ T 2 υ T 2 υ * T ) d T ,
d κ d Z = 4 β 3 κ η 2 ,
d η d Z = 2 δ η + 2 β ( 1 3 η 3 + κ 2 η ) .
d x d s = 2 x y 2 ϕ x ,
d y d s = 3 δ β y y 3 2 x 2 y ϕ y ,
ϕ = 3 δ 2 β y 2 1 4 y 4 x 2 y 2 .
d κ d Z = σ ( Z ) ,
σ ( Z ) = 0 ,
σ ( Z ) σ ( Z ) = 2 D δ ( Z Z ) ,
D = ( G ¯ 1 ) 3 N 0 1 2 Z a η ,
P Z = D 2 P κ 2 .
P ( κ , Z ) = 1 ( 2 π D Z ) 1 / 2 exp ( κ 2 4 D Z ) ,
d x d s = ϕ x + σ x ( s ) ,
d y d s = ϕ y + σ y ( s ) .
P s = x ( ϕ x P ) y ( ϕ y P ) + D x 2 P x 2 + D y 2 P y 2 .
P ( x , y , s = ) = c exp [ φ ( x , y ) D ˜ ] ,
d κ d Z = 4 δ κ + σ ( Z ) ,
κ ( Z ) κ ( Z ) = D 4 δ { exp ( 4 δ | Z Z | ) exp [ 4 δ ( Z + Z ) ] } ,
T 0 2 ( Z ) = 2 D 3 Z 3 f ( 4 δ Z ) ,
f ( x ) = 3 2 1 x 3 [ 2 x 3 + 4 exp ( x ) exp ( 2 x ) ]

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